Risk management systems are commonly employed by financial institutions, resource-based corporations, trading organizations, governments, and other users to aid in the assessment and management of risk associated with the operations of the user.
One popular example of a known risk management system is the RiskWatch V3.1.2 system, sold by the assignee of the present invention. This system allows users to employ models of financial instruments in the user's portfolio. The system evaluates the models at appropriate time intervals in view of a range of different possible scenarios. Each scenario comprises a set of values for risk factors employed in the models at each time interval, and each scenario has an assigned probability. Resulting attributes or risk values of the instruments when evaluated under each scenario at each time interval of interest are then used to produce one or more measures of risk (i.e. one or more risk metrics), which are examined to assess the risk to the user of holding the portfolio of instruments under the evaluated scenarios. One common risk value is the monetary value of the instrument or instruments under consideration, although other risk values including deltas, gammas and other computed values may also be employed. By combining these risk values appropriately, desired risk metrics can be obtained so that the user can, for example, identify opportunities for changing the composition of the portfolio, to reduce the overall risk of the portfolio or to achieve an acceptable level of risk.
Many prior art risk management systems and methods, however, require that broad simplifying assumptions (e.g. changes in certain values are normally distributed) be made for instruments which do not exist, or more specifically, for instruments which will not be created until some point in the future. This may be the case for a 90-day treasury bill (T-Bill) whose start date is two years away, for example. Simplifying assumptions must also be made for instruments for which appropriate pricing information is not available. These simplifying assumptions are made even in circumstances when such assumptions may be in conflict with the conditions that apply under one or more scenarios.
Instruments I are not limited to financial instruments and can include other instruments, including insurance instruments and commodity options, for example. While an instrument I will most commonly be a financial instrument such as a stock, bond, derivative product, or insurance product for example, generally, an instrument I may be any model which accepts one or more risk factors to simulate a characteristic of a real-world entity including the likelihood of a default by a counter party, for example.
Also, in many known risk assessment systems and methods, risk and reward are assessed on the basis of historical information, in particular, the past performance of the instruments in a portfolio. These systems and methods typically assume, explicitly or implicitly, similar performance in the future, which in some instances, leads to inaccurate results. Many risk assessment systems and methods ignore issues related to the aging of investments, which include the effects of bond coupons maturing into cash, and of the investment instruments maturing, for example. Liquidity restrictions on instruments in a portfolio, changes in market rates, credit spreads and credit downgrades can also have a significant impact on the value of a portfolio. However, the effects of market, credit, and liquidity risks and the modeling of the correlation between these types of risks are not often dealt with adequately by existing risk assessment systems and methods.
Further, evaluating the trade-off between risk and return in prior art risk management and risk assessment systems and methods may be a prohibitively time-consuming and difficult task, particularly when a user's portfolio is large.
It is known that the trade-off between risk and return can be expressed in a concise manner by means of what is known as an “efficient frontier”, which allows the optimal trade-offs between competing objectives to be identified. A classic example of this concept is the Markowitz mean-variance efficient frontier which trades off risk, as measured by variance of portfolio returns, and expected return. In this context, portfolios that earn the greatest return for a given amount of risk (or conversely, that incur the lowest risk to obtain a given level of return) are said to be efficient.
Utility theory may then be applied to determine the composition of an investor's optimal portfolio, where the portfolio is defined by a point on a constructed Markowitz efficient frontier. More specifically, given a risk-averse investor, an attainable portfolio which maximizes return for a specified level of risk and which has the highest utility for the investor lies on the efficient frontier, and can be identified using an investor's utility function. A utility function quantifies the desirability of a particular out-come, with higher values indicating greater desirability.
Although it is widely applied, the Markowitz mean-variance framework for trading off risk and reward has certain drawbacks, including its inherent assumptions that returns are normally distributed, and that portfolios are static over time. These assumptions are routinely violated, for example, by portfolios containing optionality, which in addition to displaying non-normal returns, are typically rebalanced at regular intervals. Furthermore, constructing a Markowitz efficient frontier requires one to solve a quadratic program, which can be particularly time-consuming when the subject portfolios are large.
Traditional mean-variance measures and other risk-adjusted measures which may be used to evaluate the performance of an investment, or to aid in the ranking of such investments, are also known in the prior art. For example, Morningstar's risk-adjusted rating is a measure used to rank mutual funds relative to a specified benchmark instrument (i.e. U.S. T-Bills). In measuring a mutual fund's risk, the expected losses of the mutual fund relative to the benchmark instrument are calculated and averaged. In measuring a fund's return, the difference between the cumulative value obtained by investing $1 in the mutual fund and the cumulative value obtained by investing $1 in the benchmark instrument is calculated. The relative returns for all the funds of a group are calculated by dividing each of the risk and return measures obtained by an appropriate base for the group, and may be subsequently ranked.
However, like many other traditional performance measures, the calculation of Morningstar's risk-adjusted ratings assumes that the statistics from historical frequency distributions are reliable predictors of corresponding statistics from a probability distribution of future returns. Furthermore, Morningstar's risk-adjusted ratings are often used to evaluate the performance of a single fund, and do not typically incorporate information on correlations between multiple funds in a portfolio.
Accordingly, a forward-looking risk management system, framework and methodology was developed by the assignee to provide for a more effective and efficient means of calculating performance measures and the trade-off between risk and reward for different sources of risk including market, credit, and liquidity risk, in a single, unified framework. The system, framework and methodology for determining and analyzing risk as described in U.S. patent application Ser. No. 09/323,680 addresses many of the disadvantages of prior art risk management and risk assessment systems. This system, framework and methodology will be referred to in this specification as the Mark-to-Future (MtF) framework.
The MtF framework provides a foundation on which to construct efficient frontiers and to calculate a wide variety of risk/reward performance measures. Using a scenario-based approach, the MtF framework does not place restrictions on the underlying risk factors or return distributions, and is able to incorporate effects related to the dynamic nature of portfolios, including the effects of cash settlement and active trading strategies, for example. The scenarios can be chosen to reflect not only historically-consistent events, but also extreme future possibilities that may be particularly damaging or rewarding for the portfolio. The scenarios can also be chosen to reflect the constraints imposed on investors in terms of the trades that they are able to execute. The limitations imposed by the finite liquidity of financial markets (i.e. typically, as the size of a trade increases, so too does the investor's per unit cost) can also be incorporated in an analysis within the framework.
Several scenario-based models for analyzing the trade-off between risk and reward are known in the prior art. For example, evaluation of the trade-off between a portfolio's expected profit and expected downside relative to a benchmark has been discussed in U.S. Pat. No. 5,799,287, and in Dembo and Rosen, The practice of portfolio replication: A practical overview of forward and inverse problems, Annals of Operations Research, vol. 85, 267-284 (1999).